Spin state crossover in Co3BO5
N.V. Kazak, M.S. Platunov, Yu.V. Knyazev, M.S. Molokeev, M.V. Gorev, S.G. Ovchinnikov Kirensky Institute of Physics, Federal Research Center KSC SB RAS, 660036 Krasnoyarsk, Russia Z.V. Pchelkina1,2, V.V. Gapontsev2, S.V. Streltsov1,2 1 M.N. Miheev Institute of Metal Physics UB RAS, 620137 Ekaterinburg, Russia 2Ural Federal University, 620002 Ekaterinburg, Russia J. Bartolomé3, A. Arauzo3,4 3Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza and Departamento de Física de la Materia Condensada, 50009 Zaragoza, Spain 4Servicio de Medidas Físicas, Universidad de Zaragoza, Zaragoza, Spain V.V. Yumashev Institute of Chemistry and Chemical Technology, Federal Research Center KSC SB RAS, 660036, Krasnoyarsk, Russia
S.Yu. Gavrilkin P.N. Lebedev Physical Institute of RAS, 119991 Moscow, Russia
F. Wilhelm, A. Rogalev ESRF-The European Synchrotron, 71 Avenue des Martyrs CS40220, F-38043 Grenoble Cedex 9, France
3+ Abstract We have investigated the magnetic contribution of the Co ions in Co3BO5 using the X-ray magnetic circular dichroism (XMCD) and dc magnetic susceptibility measurements. The XMCD experiments have been performed at Co K-edge in Co3BO5 and Co2FeBO5 single crystals in the fully ferrimagnetically ordered phase. The Co (K-edge) XMCD signal is found to be related to the Co2+ magnetic sublattices in both compounds providing strong experimental support for the low-spin Co3+ scenario. The paramagnetic susceptibility is highly anisotropic. An estimation of the effective magnetic moment in the temperature range 100-250 K correlates well with two Co2+ ions in the high-spin state and some orbital contribution. The crystal structure of Co3BO5 single crystal has been solved in detail at the T range 296-703 K. The unit cell parameters and volume show anomalies at 500 and 700 K. The octahedral environment and oxidation state of Co4 site strongly change with heating. The GGA+U calculations have revealed that at low-temperatures the system is insulating with the band gap of 1.4 eV and the Co2+ ions are in the high-spin state, while Co3+ are in the low-spin state. At high temperatures (T>700 K) the charge ordering disappears, and the system becomes metallic with all Co ions in 3d7 electronic configuration and high-spin state.
PACS number(s): 75.50.Gg, 75.30.Wx, 75.30.Gw
1. INTRODUCTION
The cobalt oxides belong to a large class of strongly correlated compounds showing the complex interplay between spin, charge, lattice, and orbital degrees of freedom. Like other 3d transition metals cobalt exhibits several possible oxidation states – Co2+(d7), Co3+(d6) and Co4+(d5). A property which makes the cobalt oxides very peculiar is the ability of Co3+ ions to accommodate various spin states, that is, low spin (LS), high spin (HS) and intermediate spin
1
(IS). The spin state of Co3+ appears to be very sensitive to changes in the Co-O bond length and Co-O-Co bond angle and a spin state transition could happens under action of temperature, magnetic field or external pressure. This makes the physics of the cobalt oxides very complicated being a subject of a long-standing controversy [1]. Recently, cobalt-containing oxyborates with a 2+ 3+ general formula of M 2Mʹ BO5 (M, Mʹ = Co, and 3d metal ions, as well as Al, Ga, and Mg) have attracted much attention due to the discovery of their intriguing magnetic and electronic behaviors [2-7]. These materials crystallize in orthorhombic structure (Sp.gr. Pbam) and are isostructural to ludwigite mineral. The M2+ and Mʹ3+ ions are located at the centers of edge sharing oxygen octahedra forming linear chains propagating along the short crystallographic direction (c≈3 Å). The boron atoms have a trigonal-planar coordination BO3, normally linked via common corners with oxygen octahedra. The cations occupy four crystallographically distinct metal sites 2a, 2b, 4g, and 4h, which are usually numbered as M1, M2, M3, and M4, respectively (Fig. 1). The first three are occupied by divalent metal ions, whereas the latter site located in the spaces between BO3-groups is occupied by the trivalent cations. As a result, a dense crystal structure is formed by alternating layers of divalent and trivalent cations. The triads 3-1-3 and 4- 2-4 with longest and shortest interionic distances are structurally, magnetically and electronically singled out. The common ludwigite structure allows various types of magnetic interactions involving the metal ions, including superexchange interactions, direct exchange interactions, and dipole-dipole interactions, among which the former is dominant.
a) Co2+ 4 Co3+/B3+ 3 1 3 2 4
b) c) 3 1 3 4 2 4
~3.31 Å ~2.75 Å 2
Fig. 1.a) The ab projection of crystal structure of Co3BO5. The green and blue spheres are octahedrally coordinated divalent and trivalent ions, respectively, that occupy different crystallographic sites 1, 2, 3, and 4. The triangle BO3- groups are shown by yellow. b) The triads 3-1-3 with the longest (b) and 4-2-4 with shortest Co-Co distances (c) interionic distances are highlighted by dotted lines
The homometallic ludwigites, Fe3BO5 and Co3BO5, are the most thoroughly studied systems due to their quite distinct structural, magnetic and electronic properties [2,8]. Fe3BO5 demonstrates extremely rich physics and undergoes several transitions upon cooling from room temperature. First, a structural orthorhombic – orthorhombic transition takes place at Tst = 283 K (Pbam(№55) – Pbnm(№62)), which is accompanied by the formation of the pairs (“dimers”) of 2+ 3+ Fe and Fe ions in 4-2-4 triad [9,10]. The phase transition in Fe3BO5 detected by the X-ray diffraction also manifests itself in the temperature dependence of electrical-resistivity and hyperfine parameters, revealing well-defined anomalies at Tst [9,11,12]. With decreasing temperature a cascade of magnetic transitions is observed by means of magnetometry,
Mössbauer, and temperature-dependent neutron diffraction studies [13-15]. At TN1=112 K the 4-
2-4 spin ladder is antiferromagnetically ordered. At TN2=74 K the ferrimagnetic ordering in the 3-1-3 spin-ladder appears. And finally, the transition to the antiferromagnetic ground state at
TN3=30 K with zero magnetic moment per unit cell is observed. The bulk magnetization measurements revealed that the anisotropy axis changes from the a to the b axis in the low- temperature antiferromagnetic phase.
On the contrary, cobalt ludwigite Co3BO5 demonstrates more conventional behavior, with the only ferrimagnetic transition at TN=42 K and no structural transformations [4, 16,17]. The high magnetic uniaxial anisotropy with the b-axis as an easy magnetization direction was detected in the entire temperature range [15,18]. The remanent magnetization per Co atom is ~
1.1 μB. A small slope of magnetization at high magnetic fields seems to indicate the existence of a more complex magnetic structure. Over the last decade, the attempts to understand the observed difference in magnetic and electronic properties of two homometalic ludwigites led to a synthesis of several new compounds: CoMgGaBO5 [19], Co2.4Ga0.6BO5 [20], Co2.88Cu0.12BO5 [21], Co4.76Al1.24BO5 [22],
Co2AlBO5 [23], Co3-xFexBO5 (0.0 [27], and Co5SnB2O10 [28] are some of them. (Here we do not mention ludwigites based on other 3d metal, the studies of which are also numerous). The main conclusions that can be drawn from these studies are the following: i) isovalent substitution of Co3+ ions by nonmagnetic ions like Ga and Al or magnetic Mn causes an onset of short-range or long-range orderings, but their critical temperatures are found in the vicinity of TN characteristic of Co3BO5. The reason, apparently, is 3 the sensitivity of the magnetic subsystem to the cation distribution. ii) The nonmagnetic substitution of type 2·Co3+→(Co2++M4+), where M4+=Ti or Sn leads to an antiferromagnetic spin ordering at TN=82 K, i.e. twice of TN of Co3BO5. Taking into account that tetravalent substitution generates Co2+ ions at the M4 site, an increase in the Neel temperature should be attributed to the enhancement of exchange interactions via this site. iii) An unexpected effect was discovered at the substitution of Co3+ by Fe3+ ions. In particular, with Fe3+ content increase the samples exhibit a magnetic transition at 83 K, which is then split into two magnetic transitions at 77 and 86 K, 3+ and finally, the Fe -rich sample Co2FeBO5 shows antiferromagnetic (TN1=110 K) and ferrimagnetic-like (TN2=70 K) transitions similar to the end compound Fe3BO5. An analysis of the Co-containing ludwigite systems indicates that the chemical substitution modifies the magnetically active subsystem only if it results in the appearance of magnetic ions at M4 site (Co2+, Mn3+, or Fe3+). Based on the low-temperature neutron diffraction, Freitas et.al [29] have found a rather small magnetic moment (~0.5 μB) for Co ions occupying the M4 site, instead of the expected 4 3+ 4 2 μB for high-spin Co (t2g eg , S=2), while the observed moments of Co at the M1 site (~3.6 μB), at the M2 site (3.1 μB), and at the M3 (3.8 μB) are consistent with those expected for high-spin 2+ 5 2 3+ Co ions (t2g eg , S=3/2). It was then assumed that Co ions in Co3BO5 are in the low-spin state 6 0 (t2g eg , S=0). It was found also that all magnetic moments are almost parallel to the b-axis, making it an easy magnetization direction. The spin ordering within 3-1-3 triad is antiferromagnetic (↑↓↑). These triads are ferromagnetically coupled with each other via Co ions at the M2 site resulting in the total uncompensated magnetic moment ~1.4 μB per Co ion. The recent measurements of crystal structure, magnetic susceptibility, electrical conductivity, and soft X-ray spectroscopy of Co3BO5 performed in the paramagnetic regime T=300-700 K, revealed the existence of two phase transitions at 475 and 495 K [30]. These transitions are well- defined from the differential scanning calorimetry (DSC) and electrical conductivity experiments and are accompanied by anomalies in the unit-cell parameters, although the type of crystal structure is retained and the space group remains unchanged (Pbam). A large paramagnetic moment 4.87 μB per Co ion was obtained from the fit of high-temperature part of magnetic susceptibility above room temperature and a deviation from Curie-Weiss behavior below this temperature was found. Although direct experimental evidence of spin transition is still missing, 3+ the authors of work [30] deduced that Co3BO5 undergoes a gradual Co spin-state crossover in the temperature interval TN≤T<300 K and two-step changes in the Co oxidation state in each of four crystallographic sites at high temperatures. Indeed, the effective magnetic moment μeff=4.16 μB/Co obtained from the fitting of the susceptibility in the interval T=100-300 K [16, 18] can be compared with the value μeff = 4.24 μB expected for the case in which all Co ions, including the 4 trivalent ones, are in high spin states (without orbital moment contribution). This observation indicates that a crossover or a transition from LS to HS could occur in Co3BO5. However, the study of thermodynamic properties of Co3BO5 below room temperature [16] did not reveal any anomaly except the magnetic one at TN=42K. At the same time, conductivity and differential scanning calorimetry (DSC) measurements [30] performed on both single crystalline and powder samples at T>300 K showed anomalies, which are typically associated with the first-order phase transition. However, no such phase transition is observed in Co3BO5. Consequently, the magnetic properties and origin of the magnetic moments in the Co3BO5 remains unclear. Thus, the subject of the present work is to determine the spin and oxidation states of cobalt ions in Co3BO5 and to study their evolution with temperature. We have performed single- crystalline X-ray diffraction, differential scanning calorimetry, and heat capacity measurements in a wide temperature range of 296-773 K. The Co K-edge X-ray magnetic circular dichroism (XMCD) and angle-dependent dc susceptibility experiments were carried out in the ferrimagnetic phase (~5 K) and above the magnetic phase transition (100-250 K), respectively. We calculated the electronic structure and magnetic moments of Co atoms at different metal sites for two paramagnetic phases: 296 K (low-temperature phase) 703 K (high-temperature phase) using the density-functional theory (DFT) with the account of strong Coulomb correlations through GGA+U scheme. These combined experimental and theoretical studies indicate that at temperatures up to 2+ room temperature the magnetic lattice of Co3BO5 is formed mostly by divalent Co ions (S=3/2 with a small orbital contribution). The high-temperature investigation of crystal structure did not reveal any structural transformations (sp.gr. Pbam) whereas the lattice parameters and volume show a large thermal expansion and anomalies at T1=500 and T2=700 K. The unit cell volume increases by about 4.5 %. We found that the octahedral environment and the oxidation state of Co ions at the M4 site are drastically changed, while the oxidation state of other metal sites remains unchanged. The measurements of DSC indicate that the compound does not experience any first/second-order phase transitions besides those into the magnetically ordered state at TN. This is confirmed by the thermodynamic properties measurements, which revealed the existence of two smeared anomalies in the high temperature range which are consistent with those observed in the X-ray diffraction experiments. Our GGA+U calculations have shown, first of all, that the Co2+ ions are in the high-spin state, while Co3+ are in the low-spin state at low temperatures. Second, in the high temperature phase (T=703 K) the charge ordering disappears, all Co ions have the same 3d7 electronic configuration, and the system becomes metallic with all Co ions in the high-spin state. Moreover, 5 our calculations point out that the spin-state transition and charge ordering does not necessarily occur at the same temperature. 2. EXPERIMENTAL TECHNIQUES Needle-shaped single crystalline specimens of Co3BO5 have been synthesized using a flux method in the system Bi2Mo3O12- B2O3- CoO - Nа2CO3 - Co2O3 [18]. X-ray Absorption Near-edge Structure (XANES) and X-ray Magnetic Circular Dichroism (XMCD) measurements at the K-edges of Co and Fe have been performed at the ESRF ID12 beamline. The first harmonic of APPLE-II type helical undulator was used as a source of circularly polarized X-rays. To further monochromatize the undulator emission, a fixed-exit double crystal Si(111) monochromator was used at the required photon energies. The single crystals of Co3BO5 and Co2FeBO5 were mounted on a cold finger of an “amagnetic” He flow cryostat that was inserted in a cold bore of superconducting solenoid producing a maximum magnetic field of 17 Tesla. All XANES spectra were recorded using total fluorescence yield detection mode in “back-scattering” geometry using Si photodiodes mounted on the liquid nitrogen shield of the solenoid allowing very large solid angle of detection. Experiments were performed at 5 K under a magnetic field of ±17 T to ensure that the magnetic saturation was reached. Samples were oriented so that the direction of the magnetic field and incident x-ray wavevector were collinear with the crystallographic b-axis, which is an easy magnetization direction for both samples. The normalized XANES spectra were corrected for self-absorption effects taking into account the various background contributions (fluorescence of outer electronic subshells and other elements in the sample as well as coherent and incoherent scattering) and the solid angle of the detector. The XMCD signal was obtained as direct difference of XANES spectra measured with opposite helicities of the light at a fixed magnetic field. The resulting XMCD spectra are measured repeatedly with the opposite direction of magnetization to eliminate any artifacts. For magnetic measurements a single crystal of 0.41 mg has been mounted in the rotator option of a SQUID-based magnetometer. The sample has been fixed with a pinch of vacuum grease with the rotator axis parallel and perpendicular to the needle axis (c-axis). We could select the different a-, b- and c- axis for the measurements as a function of temperature. DC Magnetic susceptibility at 1 kOe has been measured from 100 K to 250 K at different orientations. When rotating the sample at 200 K we observe a large anisotropy. The simultaneous thermal analysis (STA) of Co3BO5 sample was performed using Jupiter STA 449C analyzer (NETZSCH, Germany) equipped with an Aёolos QMS 403C quadrupole mass spectrometer (NETZSCH, Germany) in Pt-Rh crucibles. A powdered sample of Co3BO5 6 single crystals with a weight of 160 mg was used. The measurements of mass change (TG) and heat flux (DSC) was performed in sequential heating and cooling mode at a rate of 10 °C/min within temperature range 373-773 K, supplying the different gas mixtures (20 vol.% O2 in Ar and Ar with purity 99,9995 vol.%) with total flow rate of 50 cm3(NTP)/min. Two successive heating-cooling cycles were carried out for each gas mixture. The first heating-cooling cycle was used for sample conditioning and the second cycle for data processing. The specific heat capacity data from 373-773 K were obtained by the “ratio method” using a differential scanning calorimeter Netzsch STA Jupiter 449 C equipped with a special sample holder for Cp measurements. Three different runs under the same conditions (dynamic argon-oxygen atmosphere 20 vol.% O2, the heating rate 10 K/min) were carried out: (1) the baseline (empty Pt-Rh crucibles with perforated lids); (2) a standard sapphire disk (112 mg, with diameter of 6 mm and high of 1 mm) in the sample crucible; (3) the powder sample of Co3BO5 (60 mg) was manually sealed in the sample crucible. For enhancement of precise determination of heat capacity, it is advantageous when the “thermal masses” of the sapphire and the sample are approximately equivalent, i.e. (mst×Cp,st) ≈ (msa×Cp). The specific heat capacity of the sample was determined on the corrected Differential Scanning Calorimetry (DSC) curves according to equation: ( ) = ; ( ) , 푚푠푡 퐷푆퐶푠푎 − 퐷푆퐶푏푙 퐶푝 퐶푝 푠푡 where Cp,st is the tabulated specific heat푚푠푎 of 퐷푆퐶the 푠푡standard− 퐷푆퐶 푏푙at temperature T; mst, msa are masses of the standard and the sample; DSCsa, DSCst and DSCbl is the value of DSC signal at temperature T from the sample, the standard and the baseline curve, respectively. The relative error of Cp measurements did not exceed ±1%. The low-temperature part of specific heat was measured by a relaxation technique in the temperature range 2-300 K on a single crystalline sample with a mass of 3.5 mg using a commercial instrument (Quantum Design PPMS). The X-ray diffraction patterns were collected from a single crystal of Co3BO5 at 296 K, 403 K, 503 K, 603 K and 703 K using the SMART APEX II single crystal diffractometer (Bruker AXS, analytical equipment) equipped with a PHOTON 2 CCD-detector, graphite monochromator and Mo Kα radiation source. The measurements were carried out in the Common Access Facility Centre of SB RAS in Krasnoyarsk. The space group was defined by the analysis of extinction rules and intensity statistics obtained from all reflections. Multiscan absorption correction of reflection intensities was performed by SADABS program. Then, the intensities of equivalent reflections were averaged. The structure was solved by direct methods 7 [31] using the SHELXS program. The structure refinement was carried out by least-square minimization in SHELXL program [32] using anisotropic thermal parameters of all atoms. 3. DETAILS OF THE CALCULATION The electronic structure of Co3BO5 was calculated within the density-functional theory (DFT) using the Vienna Ab initio Simulation Package (VASP) [33]. The Perdew-Burke- Ernzerhof (PBE) version of the exchange-correlation potential [34] was utilized. The k-mesh with up to 225 points in the irreducible part of the first Brillouin zone was used. The total energy calculations were performed within generalized gradient approximation with account of on-site Coulomb repulsion (GGA+U) in rotationally invariant form [35]. The values of on-site Coulomb repulsion and Hund’s exchange were taken to be U =7 eV and JH =0.9 eV, respectively [36]. 4. RESULTS AND DISCUSSION 4.1. X-ray Magnetic Circular Dichroism magnetometry The element-selective XMCD spectroscopy allows to determine the magnetic behavior of the different elements in complex materials through the disentanglement of their contributions to the total magnetic response, or to compare the magnetic behavior of a chosen element in different materials. Here we focus on the isostructural compounds Co3BO5 and Co2FeBO5. 3+ 3+ In Co2FeBO5 the Fe ions substitute Co ions at M4 sites as it was found from XRD and Mössbauer spectroscopy studies [18,37]. This material has a high magnetic uniaxial anisotropy with the b-axis as an easy magnetization direction inherent to Co3BO5 and undergoes Ferri- (TN2=70 K) and AF (TN1=115 K) magnetic transitions similar to Fe3BO5 revealing a great impact of the magnetic ion at the M4 site. The Co2FeBO5 displays a strong reduction of the remanent 3+ magnetization compared to Co3BO5. Assuming the low-spin state of Co one might expect a large uncompensated magnetic moment in 4-2-4 triad, and hence in all the unit cell (this is a crude approximation since there is never the situation where all Co3+ ions are in LS), while the appearance of the ion with a nonzero magnetic moment at M4 site should result in the decrease of the moment under the condition of the antiparallel arrangement of this moment relative the 2+ host magnetic system of Co . Indeed the remanent magnetization in Co3BO5 was found to equal Mr≈72 emu/g whereas in Co2FeBO5 the Mr is reduced down to 20 emu/g [18]. Based on the neutron powder diffraction and the angle-dependent magnetization data the schematic representation of magnetic couplings in Co3BO5 and Co2FeBO5 can be presented as shown in Fig. 2. The Co3+ ion in low-spin state does not have unpaired spins ( , = 0) and, therefore, it 6 0 2+ should not contribute to the magnetic moment of Co3BO5. If this푡2 푔is푒푔 the푆 case, the Co ions, 8 2+ 3+ residing at the 3-1-3 triads and site 2 of the 4-2-4 triads, should resemble those in Co 2Fe BO5 (this is a crude approximation since the Fe3+ ion is magnetic and is certainly coupled to the Co2+ sublattice in the 4-2-4 triads). a) b) 2+ Fig. 2. Schematic representation of magnetic couplings in Co3BO5 (a) and Co2FeBO5 (b). The direction of Co and Fe3+ magnetic moments, shown by the green and blue arrows, respectively, reflects the antiferromagnetic coupling 3+ between two subsystems. The magnetic moments of Co ions located at M4 site in Co3BO5 are not shown. The solid lines denote the superexchange interactions between the nearest magnetic ions Co2+–O–Co2+ and Co2+–O–Fe3+ 2+ 3+ (Jij), while the dashed line is the magnetic coupling Co –O–Co . More detailed consideration on superexchange interactions in the ludwigites is presented in Ref. [38]. To directly address the problem of the spin state of Co3+ ions, the XMCD experiment was performed at the Co K-edge under the same temperature and field conditions on both Co3BO5 and Co2FeBO5 single crystals. The fully ferrimagnetically ordered phases were considered. The XMCD spectra are shown in Fig. 3 along with corresponding normalized XANES spectra. The pre-edge peak which is sensitive to the orbital component of the magnetic moment was analyzed. This hard X-ray spectroscopy probes the transitions from a 1s core state to the empty 4p states and the pre-edge feature (7710-7715 eV) arises from transitions to more localized unoccupied 3d states resulting from the Co4p-3d hybridization. While the shapes of Co(K) XANES spectra are very similar for both samples a significant difference in their intensity is seen. This is related to the changes of local symmetry around Co atoms. Because the cobalt local symmetry and magnetization probed by XANES/XMCD provide information averaged over all non-equivalent crystallographic positions of Co, the shape and the intensity of the spectra measured at Co K- edge is expected to be dependent on the samples. The intensity of XANES pre-edge feature is reduced in Co2FeBO5 sample relative to that of the Co3BO5 indicating both the 4p-3d hybridization and the number of the unoccupied 3d states are different. A clear XMCD signal is visible at the pre-edge feature of Co. A nonzero XMCD signal reflects the magnetic polarization of the Co 4p band resulting from the intra-atomic exchange interaction with the 3d band. The sign of the Co K-edge XMCD signal implies that in both Co3BO5 and Co2FeBO5 the magnetization of the Co sublattice is parallel to the applied magnetic field. The shape of the Co K-edge XMCD spectra is very similar for Co3BO5 and Co2FeBO5 while the signal amplitude at the pre-edge feature enhances as the Co3+ ions are replaced by Fe3+ ions. Then, we can assume 9 that the Co K-edge XMCD pre-peak (7710-7715 eV) spectrum of Co3BO5 is composed of the 2+ 2+ 3+ 3+ Co component, XMCDCo , and a contribution from Co , XMCDCo , while the XMCD signal 2+ of Co2FeBO5 depends on XMCDCo component only: 1 ( 2 ) = (2 + ) 3 2+ 3+ 푋푀퐶퐷 퐶표 퐶표 ∙ ∙ 1푋푀퐶퐷퐶표 푋푀퐶퐷퐶표 ( 2 ) = (2 ) 2 2+ The signal ratio is determined as푋푀퐶퐷 follows퐶표 퐹푒 ∙ ∙ 푋푀퐶퐷퐶표 ( 2 ) 2 = 1 + ( 2 ) 3 2 3+ 푋푀퐶퐷 퐶표 퐶표 푋푀퐶퐷퐶표 3+ ∙ � 2+� If the Co ions in Co3BO5 푋푀퐶퐷are in the퐶표 LS퐹푒 state, they should∙ 푋푀퐶퐷 not퐶표 play any significant role in the magnetic polarization of the Co(sp) band and, consequently, in the Co K-edge XMCD spectra. If this is the case, the signal ratio should be close to 0.66. Any magnetic contribution of the Co3+ ions increases this ratio. The magnitude of the XMCD signal was determined by the integration of the XMCD spectrum in the range of the quadrupole transition, and the energy interval was 7705-7715 eV. The ratio of the signals obtained in this way gives the value of 0.70±0.01. This 3+ result shows that there is a rather small net Co magnetization in Co3BO5 and this provides an experimental support for the LS state of the Co3+ ions. The small difference in signals can be explained also by the difference in the contributions of Co2+ sublattice in the direction of applied magnetic field in the two studied compounds. In the framework of the additivity model, the Co K-edge XANES spectrum of Co2CoBO5 2+ 2+ 3+ 3+ is composed of a Co component, XANESCo , and a Co one, XANESCo . We can assume 2+ that the contribution of the Co to the Co K-edge XANES spectra is the same for Co2CoBO5 and 2+ 3+ Co2FeBO5 compounds, and by subtracting XANESCo spectrum the contribution of the Co to 3+ the XANES spectrum of Co2CoBO5 can be extracted. The XANESCo spectrum obtained in this way corresponds to the Fe3+ atom substituted for Co3+ (Fig. 4a). The following noticeable 3+ features can be distinguished in XANESCo spectrum. The first one is pre-edge feature which is well resolved (the inset to Fig. 4a) and composes of two peaks at 7712.2 eV (A1) and 7714.8 (A2). Such a doublet structure was observed earlier in a wide range of XAS experimental results obtained on the perovskite-like cobaltites LaCoO3 and GdCoO3 [39, 40]. This pre-edge feature can be assigned to the 1s-3d transition, which is forbidden in the dipole approximation but it manifests itself due to the p-d orbital mixing and quadrupole contribution. The energy separation of about 2.6 eV is close to those 2.3 eV and 2.6 eV found in LaCoO3 [39, 40] and GdCoO3 [41], respectively. The next rather intensive feature arises at ~7723.3 eV (A3), followed by a sharp increase in the absorption corresponding to the main 1s-4p transition (A4) with energy position 3+ of 7732 eV. It is interesting to compare the spectrum of XANESCo in Co3BO5 with the 10 XANES at the Co K-edge for spinel ZnCo2O4 measured at the same temperature and field conditions (Fig. 4b) [42]. The latter compound is a known p-type conducting oxide material in 3+ which Co is incorporated at octahedral sites (CoOh). The Co(K-edge) XANES spectra of both materials are virtually identical showing the onset of the Co main absorption at the same energy (7732 eV). This observation clearly reveals the presence of trivalent cobalt in Co3BO5 ludwigite at low temperatures. Moreover, the shift of the main absorption to higher energies compared 3+ 2+ with that in Co2FeBO5 (7729 eV) reflects the difference in Co and Co valence states and comparable with so-called chemical shift usually observed in Co-oxides [42]. The Fe K-edge XANES/XMCD spectra recorded on Co2FeBO5 are shown in Fig. 5. XANES spectrum exhibits two main features: the pre-edge peak located at ~7115 eV, which is attributed to the Fe3+ ions occupying the octahedrally coordinated sites, and the main edge at ~7130 eV, which dominates the XMCD signal. The shape of the XMCD spectrum is different from that observed in Ho0.5Nd0.5Fe3(BO3)4 borate [43] and shows a four-peak structure: one negative and three positive ones. The peak intensity (7120 eV) reaches 0.25%. This value is about one order larger than that measured in rare-earth ferroborate and is comparable with the amplitude obtained for pure Fe foil [44], showing that Fe sublattice is nearly magnetically saturated in Co2FeBO5. Another interesting feature from the XMCD study is that it provides a simple explanation to the reduction of the magnetic moment under the substitution of Co3+ for Fe3+. The element- selective magnetization curves recorded at Co and Fe K-edges present hysteresis loops with opposite signs (Fig. 6). This observation clearly indicates an antiferromagnetic coupling between Co and Fe subsystems and is in line with our previous XMCD measurements at the L2,3 edges [45]. The Fe magnetization curve almost reaches saturation, while the Co magnetization curve has a slope highlighting the ferrimagnetic arrangement of cobalt magnetic moments in the Co2FeBO5. Besides the external magnetic field H, which determines the alignment for all magnetic moments and defines the positive direction, two exchange fields act on the Fe magnetic moments: the exchange field created by Fe spins, which favors the parallel alignment of 퐹푒−퐹푒 all Fe moments, and the 퐻푒푥 created by the Co moments. Similar contributions are acting on 퐹푒−퐶표 the Co magnetic moments:퐻푒푥 H, , . The fact that the Co magnetization has same 퐶표−퐶표 퐶표−퐹푒 orientation in both Co3BO5 and퐻 푒푥Co2FeBO퐻푒푥5, i.e. positive with respect to the applied field H, indicates that the Co magnetic subsystem determines the trend in the magnetization of the ludwigites. In the ferrimagnetic phase, where exchange fields are larger than H, the tends 퐹푒−퐶표 to align the Fe moments antiparallel to the Co ones, and consequently, to H. This퐻푒푥 magnetic coupling seems to be the strongest if we assume that ordering temperature (TN1) reflects the scale 11 of exchange interactions. As a result, the bulk magnetization of the Fe-substituted ludwigite is significantly reduced due to partial compensation of Co and Fe magnetic moments. The enhanced impact of Co contribution to the overall magnetization can be explained by 2+ the presence of a noticeable orbital moment mL of Co ion, which is only partially quenched. At low T the orientation of mL is determined by both H and the intra-atomic spin-orbit coupling HLS, which, according to Hund’s third rule, favors the parallel alignment of the orbital (mL) and spin 2+ (mS) moments of Co ion. The experimental changes in the Co K-edge XMCD for two Co-containing ludwigites, supplemented by measurements at the Fe K-edge, were found to correlate with the overall magnetism of the system Co3-xFexBO5 (x=0.0 and 1.0) and qualitatively agree quite well with the magnetic order proposed in Fig. 2. Our results underline the key role of the M4 ion because it is the filling of this site by different magnetic ions, which leads to the dramatic modification of the 3+ magnetic ground state. The XANESCo spectrum reveals features and onset of Co main absorption similar to those observed in spinel ZnCo2O4 providing the evidence of trivalent cobalt 2+ 3+ in Co3BO5. We find that it is better to view these ludwigites in terms of Co and M =Co, Fe sublattices. In summary, the XMCD measurements have shown that the magnetism of Co2+ sublattice has a similarity in two isostructural compounds Co3BO5 and Co2FeBO5, and the 3+ contribution from Co ion is strongly suppressed in Co3BO5. 1,8 0,012 Co K-edge 1,6 Co2CoBO5 0,010 5 K 1,4 Co2FeBO5 0,008 17 T 1,2 0,006 1,0 * 0,004 0,8 0,002 XANES (a.u.) 0,6 0,000 XMCD (a.u.) 0,4 -0,002 0,2 -0,004 0,0 -0,006 7700 7720 7740 7760 7780 Photon Energy (eV) Fig. 3. Normalized Co K-edge XANES/XMCD spectra recorded at T=5 K and applied field 17 T for Co3BO5 and Co2FeBO5 single crystals. The asterisk denotes the diffraction peak from the crystal. 12 1,6 a) A4 1,4 Co2CoBO5 3+ 1,2 Co K-edge Co 5 K 1,0 17 T 0,8 0,08 0,6 A2 0,04 A1 XANES (a.u.) 0,4 A3 A1A2 0,2 0,00 7710 7720 0,0 7700 7720 7740 7760 7780 Photon Energy (eV) 1,6 b) 1,4 ZnCo2O4 1,2 Co K-edge 2 K 1,0 17 T 0,8 0,6 XANES (a.u.) 0,4 0,2 0,0 7700 7720 7740 7760 7780 Photon Energy (eV) 3+ Fig. 4. a) XANES spectrum corresponding to the Co ion in Co3BO5 obtained by the subtracting of 2*XANES spectrum of Co2FeBO5 from 3*XANES spectrum of Co3BO5. b) XANES spectrum recorded at the Co K-edge for the spinel ZnCo2O4, data are taken from the Ref. [42]. 13 1,6 0,004 Co FeBO 1,4 Fe K-edge 2 5 5 K 0,003 1,2 17 T 0,002 1,0 0,8 0,001 0,6 0,000 XANES (a.u.) 0,4 XMCD (a.u.) -0,001 0,2 0,0 -0,002 7100 7120 7140 7160 Photon Energy (eV) Fig. 5. Normalized Fe K-edge XANES/XMCD spectra for Co2FeBO5 single crystals, T=5 K and applied field is 17 T 0,004 0,008 Fe 0,003 Co 0,002 0,004 0,001 5 K 0,000 0,000 -0,001 -0,004 -0,002 XMCD K-edge Fe (a.u.) XMCD Co K-edge (a.u.) -0,008 -0,003 -0,004 -20 -16 -12 -8 -4 0 4 8 12 16 20 Magnetic field (T) Fig. 6. The element-selective magnetization curves of Co2FeBO5 single crystal recorded at Co K- and Fe K-edges for applied field along the EMD (b-axis) and T=5 K. 4.2. Paramagnetic contribution of Co3BO5 as a function of crystal orientation 3+ In order to study the Co contribution in magnetism of Co3BO5 in the paramagnetic state we have performed orientation-dependent susceptibility measurements on Co3BO5 needle shaped single crystal at temperature range 100-250 K. 14 Results of the magnetic characterization measurements are presented in Fig. 7. The paramagnetic susceptibility of Co3BO5 is highly anisotropic, where the b-axis is an easy magnetization direction (EMD) and the c-axis is a hard magnetization one (HMD). The measurement in green has been done without the rotator with the needle perpendicular to field (H in the ab plane). The χ·T is relatively flat for this measurement. The measurements with the rotator have some drift which can be due to the inherent error in the background measurement which presents some orientation dependence (7-10 % deviations). This is why these curves were fitted taking into account a temperature independent contribution (inset to Fig. 7). The temperature dependence of the magnetic susceptibility in the paramagnetic state obeys the Curie–Weiss law, = + (1) 퐶 Fitting the data yields a temperature independent휒 휒0 term푇−휃 , the Curie–Weiss constant C, and the Curie–Weiss temperature collected in Table 1. 휒0 0.10 휃 10 dir_a 9 8 fit dir_a 7 dir_b 0.08 6 5 4 fit dir_b (emuK/mol) T 3 χ dir_c 2 1 fit dir_c 0.06 0 90 120 150 180 210 240 270 T(K) (emu/mol) 0.04 χ 0.02 0.00 80 120 160 200 240 T (K) Fig. 7.Temperature dependence of magnetic susceptibility for Co3BO5 single crystal in applied field oriented parallel the a,b, and c-axis. Symbols denote the experimental data, the straight lines are fitting using Eq.1. Inset: χT vs T which fitted to Eq.1 Table 1.Magnetic parameters of Co3BO5 extracted in the paramagnetic phase. χ0(emu/mol) C (emu·K/mol) θ (K) μeff(μB/f.u.) a-axis 2.4±0.2 ·10-3 3.3±0.1 22±1 5.1±1 IMD b-axis -0.6 ±0.2 ·10-3 6.1±0.1 20±1 7.0±0.1 EMD c-axis -0.2±0.1 ·10-3 4.6±0.5 -122±16 6.0±0.1 HMD The positive sign of the Curie-Weiss temperature indicates the predominance of ferromagnetic exchange interactions between Co ions in the a- and b- directions, while a strong negative 15 interaction persists inside magnetic chains propagating along the c-axis. The Curie–Weiss constant C reflects strong anisotropy in the PM state. The average value of the constant is = = 4.7±0.1 (emu·K/mol) yields an effective magnetic moment = 6.1±0.1 퐶푎+퐶푏+퐶푐 퐶per푎푣 formula3 unit, which corresponds to a moment of 3.53±0.06 per Co ion휇푒푓푓. This value휇 is퐵 much lower than the previously reported ones [16, 18]. 휇퐵 It is obvious that the magnetic moment of Co3BO5 depends on the number of magnetically active ions , , on the -factors and and on the spin values 2+ 2+ 3+ 3+ 2+ 3+ and of Co and푛퐶표 Co 푛 퐶표ions, respectively푔 : 푔퐶표 푔퐶표 2+ 3+ 푆퐶표 푆퐶표 = 2 2 (2) 2+ 2+ 2+ 2+ 3+ 3+ 3+ 3+ 푆 푛퐶표 ∙푔퐶표 ∙푆퐶표 ∙�푆퐶표 +1�+푛퐶표 ∙푔퐶표 ∙푆퐶표 ∙�푆퐶표 +1� 휇푒푓푓 � 푛퐶표2++푛퐶표3+ Assuming that all magnetic ions are in high-spin state, the spin-only magnetic moment comprises of magnetic moments of Co2+ ( =2) and Co3+ ( =1) ions with spin values of 2+ 3+ =3/2 and =2, and = 푛퐶표 =2. This gives푛 퐶표an effective spin moment of 퐻푆 퐻푆 2+ 3+ 3+ 2+ 3+ 푆퐶표 =4.24 μB/Co푆 퐶표(right panel of푔 퐶표Fig. 8).푔 If퐶표 the Co ions are in the LS state ( =0) and the 퐿푆 푆 2+ 3+ 휇Co푒푓푓 ions are still in HS state the magnetic moment is reduced to =3.16푆 퐶표μB/Co, which is 2+푠 rather close to the experimental value. Moreover, if only two Co휇푒푓푓 ions are contributing in magnetism of Co3BO5, i.e. =2 and =0, the experimentally observed effective spin 2+ 2+ 3+ 2+ moment per Co ion would be푛퐶표 4.31 μB, very푛퐶표 close to obtained values in the literature for Co in octahedral sites (4.7 – 5.2 μB) where an orbital contribution is rather important [46]. Usually, for divalent cobalt ions the observed values of the are significantly larger than 2 due to the 2+ orbital contribution. The experimental values of푔퐶표 the magnetic moments for pyroborate Co2B2O5 ( =2) [47], ludwigites Co2.5Ti0.5BO5 [27] and Co2.5Sn0.5BO휇5푒푓푓 ( =2.5) [28], 2+ 2+ 2+ kotoite Co3푛B퐶표2O6 ( =3) [48], and Co4B6O13 [49], which contain only Co ions푛퐶표 as a source of 2+ magnetism as a function푛퐶표 of the per formula unit are shown in Fig. 8. All of them show the 2+ values of very close to each푛 퐶표other and to 4.9 μB/Co , which corresponds to ≈2.5. The 2+ 2+ assumption휇푒푓푓 of spin-orbital contribution for Co ions with factor obtained above푔퐶표 will change the effective magnetic moment of Co3BO5 in two ways: i) the푔 moment has a slow increment with 3+ the increase in the nCo if Co ions are assumed to be in HS state (orange line and values above it); ii) the moment rapidly decreases if Co3+ ions are in LS state (blue line and values below). As can be seen the magnetic moment of Co3BO5 obtained at present work and in previous studies for more extended interval T≤300 K agrees well with the assumption of LS state of Co3+. Moreover, if our assumption is valid, strong ferromagnetism of Co3BO5 with magnetic moment 2+ Mr=3.4(1) μB/f.u. should be attributed to the almost collinear ferrimagnetic ordering of two Co 16 moments with g = 2.5 that is 0.91 of the expected = =3.75 per formula unit. So, one can conclude that at low temperatures (T<300푀 K)푠푎푡 the푛푔푆 value휇퐵 of effective휇퐵 magnetic moment 2+ (6.1 μB/f.u.) is compatible with two Co ions in the HS state (and some orbital contribution) and the Co3+ ions in a LS state. This fact additionally supports the results of neutron powder diffraction that only the Co2+ ions are magnetic and the Co3+ ions are in the LS state. Note, that for Co2.4Ga0.6BO5 and Co2.88Cu0.12BO5 ludwigites whose magnetic moments contain the Co2+ and a certain amount of Co3+, the falls into the range of LS values. Qualitatively, both compounds show a behavior similar휇푒푓푓 to Co3BO5 reflecting a ferrimagnetic ordering of cobalt magnetic moments near 40 K [20,21], thereby indirectly pointing out the similar nature of Co magnetism in these compounds. 2+ 4.84 µ /Co B Spin-orbital contribution Spin 5,2 [22] [47] Co2.38Al0.62(L) [48] magnetism Co2B2O5 Co3B2O6 Co Sn (L)[28] [49] 2.5 0.5 [27] Co2B3O6.5 ( ) 4,8 Co2.5Ti0.5 L [30] /Co) 4,4 µ B 4.24 /Co pr.w. B µ [20] [16,18] ( ( ) 4,0 Co2.4Ga0.6 L eff [21] Co2.88Cu0.12(L) µ 3,6 Co3+ (LS) pr.w. 3+ Co (HS) 3.16 µ /Co 3,2 B Co3BO5 2,0 2,2 2,4 2,6 2,8 3,0 n /f.u. Co Fig. 8 Magnetic moment of Co-based borates/oxyborates vs number of cobalt ions per formula unit (see text). For a better comparability, the magnetic moment data are given per one cobalt ion. The symbol (L) denotes the ludwigite. Right panel shows the values of magnetic moments per Co ion in Co3BO5 expected in the spin-only magnetism approximation. The central panel contains the values of magnetic moments assuming some orbital contribution for HS Co2+ ions: the orange line and values above are expected values for the HS Co3+ ions, while the blue line and values below are for the LS Co3+ ions in the Co-containing ludwigites. The red crosses denote the experimentally observed values of μeff for Co3BO5. 4.3. Differential scanning calorimetry The mass change (TG) and heat flux (DSC) measurements of Co3BO5 are shown in Fig. 9. The DSC-TG curves indicate that there are no changes in weight or thermal effects in a wide temperature range 373-773 K. These results show that Co3BO5 is thermally stable in the temperature range of interest. Our observation is in strong contradiction with the data of Ref. 17 [30], where two endothermic (exothermic) peaks at 472 and 493 K were found under heating (cooling) cycles and assigned to phase transitions. 0,25 100,0 0,20 0,15 99,5 0,10 Cooling O2(20%)+Ar(80%) DSC heating 0,05 O2(20%)+Ar(80%) DSC cooling O2(20%)+Ar(80%) TG heating 99,0 0,00 O (20%)+Ar(80%) TG cooling DSC (W/g) 2 TG (wt.%)TG Ar(100%) DSC cooling -0,05 Ar(100%) DSC heating Ar(100%) TG cooling 98,5 -0,10 Heating Ar(100%) TG heating -0,15 -0,20 98,0 400 450 500 550 600 650 700 750 T (K) Fig. 9. DSC-TG curves (heating-cooling cycles) showing the thermal stability of the Co3BO5 powder sample in different gas mixtures: 20 vol.% O2 in Ar and high pure Ar. 4.4. Specific heat capacity The temperature dependence of the heat capacity taken at H=0 T is shown in Fig. 10a. At low temperatures, a quite pronounced λ-type anomaly at TN=42 K implies a second-order phase transition which is in good agreement with the previously published heat capacity data [16]. In magnetic field the λ-type anomaly is progressively smeared out and shifts to higher temperatures (not shown). The above results combined with differential scanning calorimetry measurements confirmed that the title material does not exhibit a phase transitions at high temperatures in contrast to previous report [30]. For Co3BO5, the thermodynamic limit of the lattice contribution to the entropy 3Rz=224.37 J/mol K, with R=8.314 J/mol K being the gas constant and z=9 the number of atoms per formula unit, is apparently reached at 440 K. Above this temperature the specific heat Cp shows a significant contribution to the heat capacity, obviously of electronic or/and magnetic origin. To estimate the anomalous contribution of the specific heat ΔCp, we have fit the main phononic contribution to Cp(T) using Debye-Einstein approximation at temperatures well outside the region of the TN anomaly. We obtain a reasonable value of Debye temperature ΘD=493±20 K. Note, the obtained value is larger than the 140 K found in the work [16], but it is in good agreement with the values extracted for other mixed-valence oxyborates Mn2BO4 (ΘD=512 K) [50] and V2BO4 (ΘD=360 K) [51] reflecting the rigid frame of chemical bonds in borate structures. 18 The anomalous contribution ΔCp is shown in Fig. 10b. A significant anomalous contribution besides that at TN is seen in ΔCp vs T at elevated temperatures. This quite pronounced anomaly has not a jumplike shape, but a smeared one with a maximum at ~700 K and a clear shoulder at about 500 K. The best fitting of ΔCp is obtained by the sum of two Gaussians centered at 526 K and 695 K. 350 experiment a) 300 lattice fit 250 3Rz=224.37 J/mol K 200 50 40 150 30 (J/mol K) 20 p 100 C (J/mol K) 10 Θ p D=493 K 50 C 0 Θ 0 20 40 60 80 E=1113 K 0 T (K) 70 experiment b) 60 Gauss1 Gauss2 50 Sum 695 K 40 TN=42 K 30 (J/mol K) p C 20 ∆ 10 526 K 0 27 15 c) 24 12 9 21 6 7.8 J/molK 18 S (J/mol K) 3 T ∆ 0 N 15 0 25 50 75 100 12 T (K) S (J/mol K) 9 ∆ 6 3 0 0 100 200 300 400 500 600 700 800 T (K) Fig. 10. a) Temperature dependence of the specific heat in Co3BO5 measured from 2 to 300 K and from 373 to 773 K. Dotted line indicates the Dulong-Petit value. The black line refers to a phonon contribution which has been fit to 19 the data well outside the anomaly. Inset: enlarged low temperature part highlights the onset of ferrimagnetic spin ordering at TN. b) The difference of the experimental data and the phonon contribution. Besides the TN the arrows show the anomalies in specific heat obtained from the sum of two Gaussians (green and orange). c) Entropy as a function of temperature. The inset is the range of magnetic phase transition. The low temperature λ−peak entropy and enthalpy content has been calculated by 3 extrapolating its HC below TN to a T dependence, as corresponds to the spin-wave contribution -2 of a ferrimagnetic lattice, and above TN to the high-temperature T dependence, yielding to the values: a) 0 b) TN 4.4. High-temperature X-ray diffraction Several experimental studies of the Co3BO5 crystal structure have been performed [6,16,30,38,55]. Most of them consist of a structural characterization at room temperature and only works [16] and [30] are devoted to the study of temperature effects. In the latter the structural properties were studied using high-temperature X-ray powder diffraction. Here, we have performed the single-crystal X-ray diffraction measurements as a function of temperature 20 that allows determining the temperature changes in the bond-lengths and the local coordination of the Co ions. The structure determination was done at 296 K, 403 K, 503 K, 603 K, and 703 K. No conformation change was observed. The main information about crystal data, data collection and refinement are reported in Table 2. Coordinates of atoms are presented in Table 1S, while bond lengths are summarized in Table 2S of Supplemental Material [55]. The room-temperature lattice parameters are similar to those found in references [6,16,30,38,56]. For better comparability, the structural data obtained in the present work are superimposed on the data from Ref. 31 (Fig. 1S [55]). As can be seen, at room temperature the a-parameter shows a slight decrement compared with the reference data, which, however, decreases with temperature. Other lattice parameters are in good agreement with those referred. The observed difference in the a-parameter can be attributed to a small amount of metal vacancies, probably due to the peculiarities of the synthesis. Table 2.Crystallographic data and main parameters of processing and refinement Co3BO5. Crystal data Mr 267.60 Space group, Z Pbam, 4 Size, mm 0.3×0.2×0.1 T, K 296 403 503 603 703 a, (Å) 9.2742 (5) 9.2694 (4) 9.2520 (7) 9.2487 (17) 9.2676 (11) b, (Å) 11.9590 (7) 11.9902 (6) 12.0745 (9) 12.169 (2) 12.2473 (15) c, (Å) 2.9787 (2) 2.9906 (1) 3.0167 (2) 3.0314 (6) 3.0467 (4) V, (Å3) 330.37 (3) 332.38 (2) 337.01 (4) 341.18 (11) 345.81 (7) 3 Dx, Mg/m 5.380 5.348 5.274 5.210 5.140 μ, mm-1 14.770 14.681 14.479 14.302 14.111 Data collection Wavelength MoKα, λ=0.7106Å Measured 6883 6526 6754 6734 7355 reflections Independent 1058 914 953 938 1073 reflections Reflections with 848 735 728 715 713 I>2σ(I) Absorption Multiscan correction Rint 0.0697 0.0736 0.0776 0.0832 0.0968 2θmax (°) 78.31 72.36 73.04 72.20 75.88 h -15 → 15 -15 → 15 -15 → 15 -15 → 15 -15 → 15 k -20 → 20 -19 → 19 -20 → 20 -20 → 20 -21 → 20 l -5 → 5 -4 → 4 -5 → 5 -5 → 5 -5 → 5 Refinement R[F2>2σ(F2)] 0.0337 0.0309 0.0305 0.0333 0.0389 wR(F2) 0.0931 0.0657 0.0716 0.0738 0.0837 S 0.823 1.078 1.084 1.107 1.107 2 2 2 2 2 2 2 2 2 2 Weight w=1/[σ (Fo )+ w=1/[σ (Fo )+ w=1/[σ (Fo )+ w=1/[σ (Fo )+ =1/[σ (Fo )+ (0.0808P)2+ (0.0244P)2+ (0.03214P)2+ (0.0280P)2+ (0.0333P)2+ 2.653P] 0.644P] 0.380P] 0.513P] 0.796P] 21 2 2 where P=max(Fo +2Fc )/3 Extinction 0.039 (3) 0.040 (2) 0.044 (2) 0.045 (3) 0.054 (3) (∆/σ)max <0.001 <0.001 <0.001 <0.001 <0.001 3 ∆ρmax, e/Å 2.343 1.687 1.468 2.343 2.420 3 ∆ρmin, e/Å -0.817 -1.243 -1.258 -0.817 -1.411 Note, that with increasing temperature, all parameters behave similarly to those obtained in Ref. 30, demonstrating that the slope changes at about 500 K. Additionally, the a-lattice parameter shows negative thermal expansion (Fig. 11). The first anomaly at T1=500 K is clearly seen in the temperature dependences of the a, b- and c-lattice parameters and unit cell volume. With heating up the increase in the volume, ΔV/V, reaches a value of 4.5%. The thermal expansion coefficients show an initial linear regime between 300 and 400 K. Above 400 K the three coefficients (b, c, and volume) rapidly increase reaching a maximum at about T1=500 K and then grow again at T2= 700 K. 20 a) 80 b) ) -1 ) -1 , K 10 60 -6 , K -6 ( 10 a 0 ( 10 α 40 b α -10 20 300 400 500 600 700 300 400 500 600 700 140 70 c) d) 120 ) ) 60 -1 -1 , K 100 , K -6 -6 50 ( 10 ( 10 80 V c α α 40 60 300 400 500 600 700 300 400 500 600 700 T (K) T (K) Fig. 11. Temperature dependence of the expansion coefficients: a) a-parameter, b) b-parameter, c) c-parameter, d) unit cell volume. Similar to the lattice parameters, Co-O bond-lengths in Co3BO5 show an increase with temperature (Fig. 12a). The temperature has a dramatic effect on the Co2O6 and especially on the Co4O6 octahedra resulting in the rapid growth of the bond-lengths. The mean bond-lengths of Co1 and Co3 sites practically do not change with an increase in the temperature. For the analysis 22 of the local distortions, we used the Vzz parameter, which is the main component of the tensor of the electrical field gradient (EFG) produced by the different octahedral oxygen퐺훼훽 coordinations around the individual cobalt sites [26]. In Fig. 12b the main components Vzz for different cobalt sites are plotted as a function of temperature. To begin with, we consider the local distortions at room temperature. The Co2+ ions at Co1 and Co3 sites have a [2+4] coordination, forming axially compressed octahedra and, thus, showing the largest values of Vzz. Although the Co2O6 shows axial compression, it is much less than that for Co1O6 and Co3O6. Co4O6 octahedron has two short (equatorial) Co4-O1, two long (equatorial) Co4-O4 and two intermediate (axial) Co4-(O2)O3 bonds, thereby showing a slight axial elongation. The coordination bond-lengths seem to be more homogeneous around Co4 making it the most regular octahedron with smallest Vzz(4). The difference in the local deformations arises from different boron coordination. As it is seen from Fig. 13 for Co1 and Co3 sites four oxygen atoms in the equatorial plane (O3 for Co1 and O2, O5 for Co3) participate in short B-O bonds resulting in considerable elongation of appropriate bonds. However, there are only two oxygen atoms coordinated with the boron atoms in case of the Co2O6 and Co4O6 octahedra (O5 for Co2 and O2, O3 for Co4) also causing 3- elongation of the Co4-O bond in direction of the (BO3) groups. Note, the compression of Co2O6 octahedron along Co2-O5 bonds is not in line with the expected distortion. The source of this discrepancy is probably the O4 atom in the equatorial plane, which is the bridge between Co2 and Co4 atoms and participates in the simultaneous compression of the Co2-O4 and the stretching of Co4-O4 bonds. This oxygen atom has relative freedom for the displacement, which facilitates the entering of the substitution atoms (Cu, Fe, Mn, Ga, Al) into the 4-2-4 triad [20,21,22,23,26]. 2,10 ) 0,30 a b) 2,08 0,25 2,06 0,20 ) 2,04 3 0,15 ( e/A 2,02 Co1 | Co2 zz 0,10 23 3,2 c) 2.08 Co4-O3 d) Co4-O2 3,0 Co4-O1 2,8 2.04 Co4-O4 2,6 2.00 2,4 Co4-O (A) 2,2 1.96 Valence state 2,0 1.92 1,8 300 400 500 600 700 300 400 500 600 700 T (K) T (K) Fig. 12. Temperature dependences of mean bond-lengths (a), main components of EFG (b), octahedral bond-lengths 2+ 3+ in Co4O6 octahedron (c), and bond-valence sum (average among Co and Co ) for cobalt ions in Co3BO5 (d). Dashed lines show integer valence states 2+ and 3+. a) b) Fig. 13. The metal and boron coordination in Co3BO5 ludwigite. The triads Co3-Co1-Co3 (a) and Co4-Co2-Co4 (b) formed by divalent and trivalent ions are shown. The main octahedral axes along which the compression or elongation is observed are highlighted in bold. Heating up the sample above 400 K triggers a stretching of equatorial Co3-O bonds and thus indirectly a compression of equatorial Co1-O ones inside the 3-1-3 triad. In addition there is an elongation of the axial Co1-O bonds. As a result, the Co1O6 becomes more regular, while the 2+ 3+ Co3O6 shows the opposite tendency. The other subsystem formed by Co and Co in sites 2 and 4 behaves in a different way. Above 400 K the local distortion of the Co4 site rises sharply 2+ while the Vzz(2) for Co ions drops. As a result, the difference in the octahedral environments of two metal sites decreases and becomes negligible at 703 K. The thermal variations of the Co4O6 24 bond-lengths are shown in Fig. 12c. It is clearly seen that the axial bonds, directed along BO3 groups, grow much faster than equatorial ones resulting in the dramatic changes in Vzz. To evaluate the oxidation states of different Co ions, a bond-valence-sum (BVS) approach has been applied [57]. The room-temperature oxidation states of Co1, Co2, and Co3 suggest that these sites are occupied by the Co2+ ions, whereas the Co4 site is filled by Co3+ (atomic charges 2.78(6)/2.84(7) when bond valence parameters are related to Co2+/Co3+ oxidation state) (Table 3). With temperature increases the valence bond charges for Co1, Co2, and Co3 sites tend to stay in the vicinity of +2, while the valence state of Co4 site drastically decreases (Fig. 12d). At T=703 K the empirical estimates predict atomic charges of 2.25(9)/2.30(7) for Co4. These values indicate propensity of site Co4 to shelter Co2+ at high temperature phase. The empirical estimates of the valence for boron site are consistent with +3. The oxygen atomic charges show a clear decrement with temperature increase. Table 3. Oxidation states of the metal and oxygen ions in Co3BO5 obtained using the BVS approach, 2+ 3+ 3+ R0(Co )=1.692 Å, R0(Co )=1.700 Å, R0(B )=1.371 Å, and b=0.37. 296 K 703 K Co2+/Co3+ Co2+/Co3+ Co1 2.06(3)/2.10(8) 2.05(3)/2.09(8) Co2 2.27(8)/2.32(8) 2.10(3)/2.14(9) Co3 2.12(2)/2.16(9) 2.09(0)/2.13(5) Co4 2.78(6)/2.84(7) 2.25(9)/2.30(7) B 2.95(7) 2.94(6) O1 1.99(0) 1.85(5) O2 1.98(9) 1.87(0) O3 2.05(8) 1.96(3) O4 1.95(5) 1.78(0) O5 2.10(5) 1.95(3) For the future discussion, note that we have observed negative thermal expansion of a- parameter in other homometallic oxyborate Mn2BO4 within the same T interval (300-500 K) [58]. The warwickites and ludwigites have strong structural affinities and belong to the “3Å wall-paper structures”. In both compounds the planar BO3 triangles parallel to (110) plane connect adjacent layers of metal ions in [100] direction by corner-sharing. In ludwigites M4 sites 3+ located in the voids between the BO3-tunnels are filled by M ions, whereas in warwickites similar sites are occupied by both di- and trivalent ions. From the crystal-chemical background it can be expected that the structure should be more rigid in the a-direction due to the rigidity of the bonds within the boron group and that the thermal/substitution effects should be more pronounced in b- and c- directions. This is confirmed by the comparison of values of thermal 25 expansion coefficients for both materials. So, we can assume that the observed anomalies of a- parameters result from the structural peculiarities of the oxyborate family. At the same time the thermal expansion coefficients of b-, c-, and unit cell have non- monotonic dependence on the temperature, going through a maximum at T1=500 K where heat capacity and conductivity show the anomalies. This correlates with a rapid increase in the octahedral Co-O distances at Co4 site, occupied by Co3+ and points out a manifestation of another mechanism of lattice expansion besides the conventional lattice anharmonicity. This mechanism can be attributed to the spin fluctuations arising from the change in the ionic radius of Co3+ ion at spin-state transition from LS to HS. It is instructive to compare the LS-HS 3+ transition of the Co ion discussed here with simpler perovskite rare-earth cobaltites LnCoO3 (Ln=La, Dy, Sm, Gd, …) [59,60,61 and herein]. In LaCoO3 a spin-state transition is well known and reveals itself with a sharp peak in the magnetic susceptibility at 150 K and smooth metallization above 500 K [62,63]. The maximum thermal expansion coefficient results from strong thermal fluctuations of the Co3+ ions multiplicity between the low and high spin terms. All thermodynamic properties including the thermal expansion, magnetic susceptibility, specific heat are correlated with the spin-state transition in rare-earth cobaltites [64]. Moreover, maxima in the thermal expansion and magnetic susceptibility are related to the maximal rate of the multiplicity fluctuations when the derivative of the concentration of thermally excited HS terms dnHS/dT has maximum. This comparison indicates that in the Co3BO5 the maximal rate of the multiplicity fluctuations occurs at the temperature close to T1=500 K. Upon further heating a clear anomaly is revealed in the temperature dependences of the expansion coefficients and the heat capacity with the maximum at T2=700 K. Using the same methodology as for perovskite- like cobaltites, the observed anomaly can be associated with the smooth electronic transition caused by the modification of electronic structure. The conductivity data on Co3BO5 presented in Ref. [30] shows a gradual increase in σ(T) up to the highest measured temperature of 505 K. The electrical measurements data at elevated temperatures are not currently available. The electron count in a triad 4-2-4 corresponds to three Co3+ ions with one extra electron per triad. This itinerant electron can be localized at Co2 site, smeared over all three sites, or distributed between two adjacent Co2-Co4 sites leading to the dimerization state. In the Fe3BO5 a dimer formation at the 4-2-4 ladder is associated with structural phase transition and change in space group from Pbam(№55) to Pbnm(№62) at TST=283 K [9,10]. Neither present nor previous XRD studies reveal any structural phase transition over the entire investigated temperatures confirming the absence of the dimerization of the 4-2-4 triad in Co3BO5. Nevertheless, the spatial distribution for Co oxidation states in the system is dramatically changed leading to the electronic transition. The room-temperature BVS calculations clearly indicate the localized 26 character of 3d electrons at Co2 and Co4 sites (the atomic charges are about +2.29 and +2.81, respectively) highlighting the charge ordering. Upon heating the oxidation state of Co4 site first decreases rapidly within T range 400-500 K and then more slowly, while the oxidation states of the rest of cobalt sites are almost unchanged. The increase in temperature was found to suppress the charge-ordered phase by means of squeezing out the excess charge from the Co4 octahedra. As a result, at 703 K all metal sites in the lattice become occupied by divalent ions, which inevitably should lead to the occurrence of some amount of holes at oxygen atoms. This effect manifests itself in the decrement of the oxygen atomic charges, most noticeable for O4 site. Now, Co2 and Co4 site are no longer distinguished but they become equivalent from the point of view of both octahedral distortions and atomic charges leading to the quenching of the charge ordering. This transition is not associated with the redox process, as one can see from DSC measurements, where the sample shows thermal stability over the measured temperature range, but it is more likely that it can be considered as an electronic transition caused by the reorganization of the electronic structure of Co3BO5. The electron transition found from X-ray diffraction involves not only metal sites but also oxygen ones in the lattice and should be seen from the heat-capacity, conductivity and spectroscopic measurements. The next finding is that the observed effective moment = 4.87 μB extracted from high-temperature range T=500-700 K [30] can be reasonably explained.휇푒푓푓 Indeed, if we assume that at high temperatures all cobalt ions become a divalent =3 and have some orbital moment inherent in Co2+ then =4.84 2+ 2+ μB/Co (left panel of Fig.푛퐶표 8). 휇푒푓푓 Within the ternary system Co-B-O, the following borate/oxyborates were obtained at ambient pressure Co2B2O5 [47], Co3B2O6 [48], Co3BO5 [4], Co4B6O13 [49], α-CoB4O7 [65], and β-CoB4O7 [66] and HP-CoB2O4 [67] that require high pressure. Of these, only ludwigite contains trivalent cobalt ions. More interesting is that other 3d transition metals Fe, Mn, V, Cr, Ti form III III II III M -B-O systems isotypic calcite (M BO3) [68-71], warwickite (M M OBO3) [50,51], II III III ludwigite (M 2M O2BO3) [3,8,72], and norbergite (M 3BO6) [73,74,75]. This comparison indicates a clear tendency for cobalt systems to shelter Co2+ ions. The thermal instability of Co3+ in the borate systems requires additional study. Another aspect that we would like to discuss is the effect of M4 ion on the long-range crystal structure. While the influence of M4 ion on the magnetic order in the ludwigites was discussed in Sections 4.1. and 4.2., here, we focus on the available structural data on the Co- based ludwigites. Taking the mean bond-length Co3BO5 vs T [p.w.] Co2.4Ga0.6BO5 [21] Co Cu BO [22] 2.88 0.12 5 Co1.7Mn1.3BO5 [27] 12,4 9,42 Co3-xFexBO5 [26] 12,3 9,39 Co2FeBO5 [19] Co Sn BO [29] 9,36 2.5 0.5 5 12,2 Co2.5Ti0.5BO5 [28] 9,33 a (A) b (A) 12,1 9,30 703 K 12,0 9,27 296 K 9,24 11,9 3,12 3,10 360 3,08 355 3,06 350 ) 3 3,04 345 c (A) 3,02 340 V (A 3,00 335 2,98 330 2,96 325 1,96 1,98 2,00 2,02 2,04 2,06 2,08 2,10 1,96 1,98 2,00 2,02 2,04 2,06 2,08 2,10 4.5. Results of the DFT+U calculations To understand the obtained results and determine the magnetic and electronic structure of Co3BO5, complementary theoretical studies have been carried out. The calculations were done using the GGA+U approach for both low- and high-temperature phases. For this the crystal structures corresponding to T=296 and 703 K, respectively, obtained in our X-ray diffraction experiments and magnetic structure determined in Ref. [29] were utilized. Thanks to the ability of the GGA+U approach to stabilize different solutions corresponding not only to the global, but also different local minima of the density functional, we calculated 28 total energies of two configurations, where Co4 ion is either magnetic or not (these configurations were obtained in conventional self-consistent DFT+U calculations without any constrains). These configurations are dubbed as ↓↑↑↓ or ↓↑↑0, where ↑ stands for spin up and ↓ for spin down and the order of signs corresponds to labels of the Co ions. We found that the low temperature phase ↓↑↑0 configuration with nearly nonmagnetic Co4 ions has the lowest total energy, while ↓↑↑↓ solution is 46.88 meV per cell (12 Co ions) or 11.72 meV per Co4 ion higher in energy. Taking into account that the calculations were performed for the structure corresponding to T=296 K one may expect that this configuration can be thermally excited at temperatures ~432 K, i.e. close to the first anomaly in unit cell parameters observed experimentally. Careful analysis of the occupation matrixes shows that there is a charge ordering in this low temperature phase: Co1, Co2, and Co3 are 2+ and have 3d7 electronic configuration, while Co4 is 3+ with six 3d electrons in both solutions. Moreover, Co4 ion is in the low-spin state in ↓↑↑0 and the high-spin state in ↓↑↑↓ configuration. List of magnetic moments on each Co ion can be found in Tab. 4. The density of states plots for both configurations are shown in Fig. 15. One may see that the system is insulating with the band gap of 1.4 eV for ↓↑↑0 configuration corresponding the ground state. This is rather important since the spin-state transition by itself does not lead to the metal-insulator transition. As we will show below only breaking of the charge ordering results in formation of a metallic state. The obtained value of the insulating gap is in reasonably good agreement with the experimental value of Eg = 2·Ea ≈ 1.7 eV previously found from conductivity measurements below room temperature [76]. On another hand, we see that the charge ordering is not susceptible to the spin state of Co4 ion: in both calculated configurations this ion adopts 3+ charge state. Moreover, we performed additional calculations of other magnetic structures and obtained that even in fully ferromagnetic state Co4 ions are in 3d6 electronic configuration. Thus, we see that the mechanism of charge disproportionation is related with features of the crystal structure. 29 Fig. 15. Co3BO5 total DOS for LT and HT phases. Table 4. Magnetic moment (μB) of Co ions in Co3BO5 obtained for high- and low-temperature phases in the GGA+U calculations. R(L)T phase HT phase ↓↑↑↓ ↓↑↑0 ↓↑↑↓ ↓↑↑0 Co1 2.8 2.8 2.8 2.8 Co2 2.8 2.7 2.8 2.8 Co3 2.8 2.8 2.8 2.8 Co4 3.2 0.2 2.6 0.2 As it has been explained above local surroundings of the Co1 and Co3 are very different from Co2 and Co4. There are four O2- ions having bonds with B3+ ions for Co1 and Co4 ions, but only two for Co2 and Co4. Then, effective electrostatic field acting on the Co1 and Co3 is weaker and already from these geometrical arguments one may expect that average Co-O distances for these ions should be longer than for Co2 and Co4 and, thus, Co1 and Co3 are prone to be 2+. This type of reasoning fully agrees with actual experimental Co-O bond distances, presented in Fig. 12. From the same Fig. 12 we see that this is Co4 ion, which has the smallest average Co-O bond length and may adopt 3+ charge state, which ionic radius (for any spin-state) is less than the one of Co2+ ions. However, with increase of the temperature the difference between average Co-O bond distances for different Co ions nearly vanishes destabilizing charge ordering. Our GGA+U 30 calculations for the high temperature phase show that the charge ordering does disappear, all Co ions have 3d7 electronic configuration, and the system becomes metallic in the ↓↑↑↓ configuration (see Fig. 15), which now has the lowest total energy. Disappearance of the charge ordering may explain the experimentally observed increase of electrical conductivity [31]. It has to be mentioned that with given chemical formula one cannot have an insulating state with all Co ions being 2+, while in case of metal this is possible. But if such a state will be probed by, e.g., X-ray spectroscopy then there must be seen a lot of ligand holes, compensating 2+ valence state. 5. CONCLUSION We have studied the electronic and magnetic state of single-crystalline Co3BO5 using X- ray magnetic circular dichroism, magnetic susceptibility, X-ray diffraction, differential scanning calorimetry, and heat capacity measurements. The experiments were done in a wide temperature interval covering both magnetically ordered and paramagnetic phases. The Co K-edge 3+ XANES/XMCD experiments were performed in a ferrimagnetic state. The extracted XANESCo 3+ spectrum is an experimental evidence of the Co ions in Co3BO5. The Co sublattice magnetism 3+ has a similarity in two isostructural compounds Co3BO5 and Co2FeBO5, in the latter the Co ions are replaced by Fe3+ ones. The rather small contribution from Co3+ ion to XMCD signal of Co3BO5 is indicative of the LS state of this ion. The Co and Fe K-edges XMCD measurements recorded in the Co2FeBO5 single crystal have uncovered an antiferromagnetic coupling between the two sublattices, which indicates the generality of the formation of magnetic structures in 2+ Co3BO5 and Co2FeBO5, namely the ferrimagnetic arrangement of Co moments and antiferromagnetic arrangement of their moment relative to the magnetic moment at the M4 site. The sample-oriented measurements of magnetic susceptibility have revealed that a magnetic behavior of Co3BO5 in the paramagnetic regime (T<300 K) is dominated by the high uniaxial 2+ anisotropy. The effective magnetic moment 6.1 μB/f.u. is compatible with two Co ions in the HS state and orbital contribution. Our measurements of the thermodynamic properties of Co3BO5 have explored two anomalies at T1≈500 and T2≈700 K besides the magnetic phase transition at TN. In contrast to work [30] the high-temperature anomalies we observed in Co3BO5 are smooth, which indicates that they are not first/second-order phase transitions. In line with this finding, our DSC study of the single crystal heated up to 770 K, confirmed that the sample is thermally stable. These anomalies detected by heat-capacity also manifested itself in the X-ray diffraction measurement, which reveals well-defined maxima of thermal expansive coefficients. We also observed a remarkable sensitivity of Co4 octahedral site to the temperature effect consisting in the change of the octahedral distortion and the oxidation state. With the increase in temperature the difference 31 between Co2 and Co4 sites nearly vanishes making them equivalent. This is an electronic transition that is not caused by electron-sharing between the metal atoms in 4-2-4 triad as it was proposed in case of Fe3BO5 at TCO, but it is a consequence of the transition of the charge excess from Co4 metal site to the oxygen atoms (charge transfer). The available data do not allow determining whether the spin transition and the electronic transition occur simultaneously or they are spaced apart in temperature. The GGA+U calculations show that at the low-temperature phase the Co3BO5 is an insulator with the band gap of 1.4 eV, the ground state is ferrimagnetic with Co3+ ion is being in LS state. At high temperature the charge ordering does disappear, all Co ions have 3d7 electronic configuration, and the system becomes metallic. ACKNOWLEDGMENTS Natalia Ivanova’s and Leonard Bezmaternykh's memory is dedicated. The authors acknowledge A. Ney for the allow us to use XANES spectrum of ZnCo2O4 film. We are grateful to the Russian Foundation for Basic Research (project no. 20-02-00559), and President Council on Grants (project no. МК-2339.2020.2) for supporting our work. This research was carried out within the state assignment of the Russian Ministry of Science and High Education via program “Quantum'' (No. AAAA-A18-118020190095-4). We also acknowledge support by Russian Ministry of Science via contract 02.A03.21.0006. We acknowledge financial support from the Spanish MINECO DWARFS project MAT2017-83468-R, and Gobierno de Aragón (RASMIA group, E12-17R). REFERENCES 1. J.B. Goodenough, J. Phys. Chem. Solids 6, 287 (1958). 2. R.B. Guimaraes, M. Mir, J.C. Fernandes, M.A. Continentino, H.A. Borges, G. Cernicchiaro, M.B. Fontes, D.R.S. Candela, and E. Baggio-Saitovitch. "Cation-mediated interaction and weak ferromagnetism in Fe3O2BO3." Physical Review B 60, no. 9 (1999): 6617. 3. R. Norrestam, K. Nielsen, I. Søtofte, and N. Thorup. "Structural investigation of two synthetic oxyborates: the mixed magnesium-manganese and the pure cobalt ludwigites, Mg1.93Mn1.07O2BO3 and Co3O2BO3." Zeitschrift für Kristallographie-Crystalline Materials 189, no. 1-4 (1989): 33-42. 4. N.B. Ivanova, A.D. Vasil’ev, D.A. Velikanov, N.V. Kazak, S.G. Ovchinnikov, G.A. Petrakovskiĭ, and V.V. Rudenko. "Magnetic and electrical properties of cobalt oxyborate Co3BO5." Physics of the Solid State 49, no. 4 (2007): 651-653. 32 5. J.C. Fernandes, R.B. Guimaraes, M.A. Continentino, H.A. Borges, A. Sulpice, J.L. Tholence, J.L. Siqueira, L.I. Zawislak, J.B.M. Da Cunha, and C.A. Dos Santos. "Magnetic interactions in the ludwigite Ni2FeO2BO3." Physical Review B 58, no. 1 (1998): 287. 6. R. Norrestam, M. Kritikos, K. Nielsen, I. Søtofte, and N. Thorup. "Structural characterizations of two synthetic Ni-ludwigites, and some semiempirical EHTB calculations on the ludwigite structure type." Journal of Solid State Chemistry 111, no. 2 (1994): 217-223. 7. M. Onoda. "Crystal Structure and Electronic State of the Disordered S=1 System (LixV1−x)3BO5 with x 0.3." Journal of Solid State Chemistry 141, no. 2 (1998): 418-423. 8. J.C. Fernandes, R.B.≃ Guimarães, M.A. Continentino, L. Ghivelder, and R.S. Freitas. "Specific heat of Fe3O2BO3: Evidence for a Wigner glass phase." Physical Review B 61, no. 2 (2000): R850. 9. M. Mir, R.B. Guimarães, J.C. Fernandes, M.A. Continentino, A.C. Doriguetto, Y.P. Mascarenhas, J. Ellena, E.E. Castellano, R.S. Freitas, and L. Ghivelder. "Structural Transition and Pair Formation in Fe3O2BO3." Physical review letters 87, no. 14 (2001): 147201. 10. M. Mir, M., Jan Janczak, and Y. P. Mascarenhas. "X-ray diffraction single-crystal structure characterization of iron ludwigite from room temperature to 15 K." Journal of applied crystallography 39, no. 1 (2006): 42-45. 11. A.P. Douvalis, A. Moukarika, T. Bakas, G. Kallias, and V. Papaefthymiou. "Mössbauer and magnetization studies of Fe3BO5." Journal of Physics: Condensed Matter 14, no. 12 (2002): 3303. 12. J.J. Larrea, D.R. Sanchez, F.J. Litterst, E.M. Baggio-Saitovitch, J.C. Fernandes, R.B. Guimaraes, and M.A. Continentino. "Magnetism and charge ordering in Fe3O2BO3 studied by 57 Fe Mössbauer spectroscopy." Physical Review B 70, no. 17 (2004). 13. J.P. Attfield, J.F. Clarke, and D.A. Perkins. "Magnetic and crystal structures of iron borates." Physica B: Condensed Matter 180 (1992): 581-584. 14. P. Bordet and E. Suard. "Magnetic structure and charge ordering in Fe3BO5: A single-crystal x-ray and neutron powder diffraction study." Physical Review B 79, no. 14 (2009): 144408. 15. J. Bartolomé, A. Arauzo, N. V. Kazak, N. B. Ivanova, S. G. Ovchinnikov, Yu V. Knyazev, and I. S. Lyubutin. "Uniaxial magnetic anisotropy in Co2.25Fe0.75O2BO3 compared to Co3O2BO3 and Fe3O2BO3 ludwigites." Physical Review B 83, no. 14 (2011): 144426. 16. D.C. Freitas, M.A. Continentino, R.B. Guimaraes, J.C. Fernandes, J. Ellena, and L. Ghivelder. "Structure and magnetism of homometallic ludwigites: Co3O2BO3 versus Fe3O2BO3." Physical Review B 77, no. 18 (2008): 184422. 33 17. N.V. Kazak, N.B. Ivanova, O.A. Bayukov, S.G. Ovchinnikov, A.D. Vasiliev, V.V. Rudenko, J. Bartolomé, A. Arauzo, and Yu.V. Knyazev. "The superexchange interactions in mixed Co–Fe ludwigite." Journal of Magnetism and Magnetic Materials 323, no. 5 (2011): 521-527. 18. N.B. Ivanova, N.V. Kazak, Yu.V. Knyazev, D.A. Velikanov, L.N. Bezmaternykh, S.G. Ovchinnikov, A.D. Vasiliev, M.S. Platunov, J. Bartolomé, and G.S. Patrin. "Crystal structure and magnetic anisotropy of ludwigite Co2FeO2BO3." Journal of Experimental and Theoretical Physics 113, no. 6 (2011): 1015-1024. 19. N.B. Ivanova, M.S. Platunov, Yu.V. Knyazev, N.V. Kazak, L.N. Bezmaternykh, E.V. Eremin, and A.D. Vasiliev. "Spin-glass magnetic ordering in CoMgGaO2BO3 ludwigite." Low Temperature Physics 38, no. 2 (2012): 172-174. 20. N.B. Ivanova, M.S. Platunov, Yu.V. Knyazev, N.V. Kazak, L.N. Bezmaternykh, A.D. Vasiliev, S.G. Ovchinnikov, and V.I. Nizhankovskii. "Effect of the diamagnetic dilution on the magnetic ordering and electrical conductivity in the Co3O2BO3:Ga ludwigite." Physics of the Solid State 54, no. 11 (2012): 2212-2221. 21. N.B. Ivanova, N.V. Kazak, Yu.V. Knyazev, D.A. Velikanov, A.D. Vasiliev, L.N. Bezmaternykh, and M.S. Platunov. "Structure and magnetism of copper-substituted cobalt ludwigite Co3O2BO3." Low Temperature Physics 39, no. 8 (2013): 709-713. 22. C.P.C. Medrano, D.C. Freitas, E.C. Passamani, C.B. Pinheiro, E. Baggio-Saitovitch, M.A. Continentino, and D.R. Sanchez. "Field-induced metamagnetic transitions and two- dimensional excitations in ludwigite Co4.76Al1.24(O2BO3)2." Physical Review B 95, no. 21 (2017): 214419. 23. J. Kumar, S.N. Panja, D.J. Mukkattukavil, A. Bhattacharyya, A.K. Nigam, and S. Nair. "Reentrant superspin glass state and magnetization steps in the oxyborate Co2AlBO5." Physical Review B 95, no. 14 (2017): 144409. 24. D.C. Freitas, M.A. Continentino, R.B. Guimaraes, J.C. Fernandes, E.P. Oliveira, R.E. Santelli, J. Ellena, G.G. Eslava, and L. Ghivelder. "Partial magnetic ordering and crystal structure of the ludwigites Co2FeO2BO3 and Ni2FeO2BO3." Physical Review B 79, no. 13 (2009): 134437. 25. N.V. Kazak, Yu.V. Knyazev, M.S. Platunov, А.О. Vasiliev, L.N. Bezmaternykh, V.V. Rudenko, N.B. Ivanova, J. Bartolome, А. Arauzo, and S.G. Ovchinnikov. “Electronic and magnetic states of the Co and Fe in ludwigite system Co3-xFexBO5” VII Euro-Asian symposium “Trends in MAGnetism”, Ekaterinburg, Russia p.57 (2019). 26. Yu.V. Knyazev, N.B. Ivanova, N.V. Kazak, M.S. Platunov, L.N. Bezmaternykh, D.А. Velikanov, А.D. Vasiliev, S.G. Ovchinnikov, and G.Yu. Yurkin. "Crystal structure and 34 magnetic properties of Mn substituted ludwigite Co3O2BO3." Journal of magnetism and magnetic materials 324, no. 6 (2012): 923-927. 27. D.C. Freitas, R.B. Guimaraes, D.R. Sanchez, J.C. Fernandes, M.A. Continentino, J. Ellena, A. Kitada et al. "Structural and magnetic properties of the oxyborate Co5Ti(O2BO3)2." Physical Review B 81, no. 2 (2010): 024432. 28. C.P.C. Medrano, D.C. Freitas, D.R. Sanchez, C.B. Pinheiro, G.G. Eslava, L. Ghivelder, and M.A. Continentino. "Nonmagnetic ions enhance magnetic order in the ludwigite Co5Sn(O2BO3)2." Physical Review B 91, no. 5 (2015): 054402. 29. D.C. Freitas, C.P.C. Medrano, D.R. Sanchez, M. Nunez Regueiro, J.A. Rodríguez- Velamazán, and M.A. Continentino. "Magnetism and charge order in the ladder compound Co3O2BO3." Physical Review B 94, no. 17 (2016): 174409. 30. C.W. Galdino, D.C. Freitas, C.P.C. Medrano, R. Tartaglia, D. Rigitano, J.F. Oliveira, A.A. Mendonça et al. "Magnetic, electronic, structural, and thermal properties of the Co3O2BO3 ludwigite in the paramagnetic state." Physical Review B 100, no. 16 (2019): 165138. 31. G.M. Sheldrick. A short history of SHELX. ActaCryst. A, Vol. 64, issue 1 (2008) pp.112- 122. 32. Sheldrick, G. M. SHELXS and SHELXL97. Program for Crystal Structure Refinement, University of Göttingen, Germany (1997). 33. G. Kresse and J. Furthmuller, Phys. Rev. B, 54, 11169 (1996). 34. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett., 77, 3865 (1996). 35. A.I. Liechtenstein, V.I. Anisimov and J. Zaanen, Phys. Rev. B, 52, R5467 (1995). 36. M.M. Markina, B.V. Mill, E.A. Zvereva, A.V. Ushakov, S.V. Streltsov, and A.N. Vasiliev, Phys. Rev. B, 89, 104409 (2014). 37. Yu.V. Knyazev, N.B. Ivanova, O.A. Bayukov, N.V. Kazak, L.N. Bezmaternykh, and A.D. Vasiliev. "Evolution of the mössbauer spectra of ludwigite Co3−xFexO2BO3 with substitution of iron for cobalt." Physics of the Solid State 55, no. 6 (2013): 1175-1179. 38. Yu.V. Knyazev, N.V. Kazak, I.I. Nazarenko, S.N. Sofronova, N.D. Rostovtsev, J. Bartolomé, A. Arauzo, and S. G. Ovchinnikov. "Effect of magnetic frustrations on magnetism of the Fe3BO5 and Co3BO5 ludwigites." Journal of Magnetism and Magnetic Materials 474 (2019): 493-500. 39. G. Thornton, I.W. Owen, and G.P. Diakun. "The two-band model of the LaCoO3 semiconductor-metal transition: a spectroscopic evaluation." Journal of Physics: Condensed Matter 3, no. 4 (1991): 417. 40. O. Haas, R.P. W. J. Struis, and J. M. McBreen. "Synchrotron X-ray absorption of LaCoO3 perovskite." Journal of Solid State Chemistry 177, no. 3 (2004): 1000-1010. 35 41. V.A. Dudnikov, N.V. Kazak, Yu.S. Orlov, S.N. Vereshchagin, S.Yu Gavrilkin, A.Yu Tsvetkov, M.V. Gorev et al. "Structural, Magnetic, and Thermodynamic Properties of Ordered and Disordered Cobaltite Gd0.1Sr0.9CoO3–δ." Journal of Experimental and Theoretical Physics 128, no. 4 (2019): 630-640. 42. Bastian Henne, Verena Ney, Katharina Ollefs, Fabrice Wilhelm, Andrei Rogalev, and Andreas Ney. "Magnetic interactions in the Zn-Co-O system: tuning local structure, valence and carrier type from extremely Co doped ZnO to ZnCo2O4." Scientific Reports 5 (2015): 16863. 43. M. Platunov, N. Kazak, V. Dudnikov, V. Temerov, I. Gudim, Yu. Knyazev, S. Gavrilkin et al. "Element selective magnetism in Ho0.5Nd0.5Fe3(BO3)4 single crystal probed with hard X- ray magnetic circular dichroism." Journal of Magnetism and Magnetic Materials 479 (2019): 312-316. 44. O. Mathon, F. Baudelet, J-P. Itié, S. Pasternak, A. Polian, and S. Pascarelli. "XMCD under pressure at the Fe K edge on the energy-dispersive beamline of the ESRF." Journal of synchrotron radiation 11, no. 5 (2004): 423-427. 45. M.S. Platunov, S.G. Ovchinnikov, N.V. Kazak, N.B. Ivanova, V.N. Zabluda, E. Weschke, E. Schierle, and K.V. Lamonova. "Identification of local magnetic contributions in a Co2FeBO5 single crystal by XMCD spectroscopy." JETP letters 96, no. 10 (2013): 650-654. 46. R.L. Carlin. Magnetochemistry. Springer Science & Business Media, 2012. 47. T. Kawano, H. Morito, and H. Yamane. "Synthesis and characterization of manganese and cobalt pyroborates: M2B2O5 (M= Mn, Co)." Solid state sciences 12, no. 8 (2010): 1419- 1421. 48. N.V. Kazak, M.S. Platunov, N.B. Ivanova, Yu.V. Knyazev, L.N. Bezmaternykh, E.V. Eremin, A.D. Vasil’ev et al. "Crystal structure and magnetization of a Co3B2O6 single crystal." Journal of Experimental and Theoretical Physics 117, no. 1 (2013): 94-107. 49. H. Hagiwara, H. Sato, M. Iwaki, Y. Narumi, and K. Kindo. "Quantum magnetism of perfect spin tetrahedra in Co4B6O13." Physical Review B 80, no. 1 (2009): 014424. 50. N.V. Kazak, M.S. Platunov, Yu.V. Knyazev, E.M. Moshkina, S.Yu. Gavrilkin, O.A. Bayukov, M.V. Gorev et al. "Fe-induced enhancement of antiferromagnetic spin correlations in Mn2−xFexBO4." Journal of Magnetism and Magnetic Materials 452 (2018): 90-99. 51. E.M. Carnicom, K. Górnicka, T. Klimczuk, and R.J. Cava. "The homometallic warwickite V2OBO3." Journal of Solid State Chemistry 265 (2018): 319-325. 52. D.G. Onn, Horst Meyer, and J. P. Remeika. "Calorimetric study of several rare-earth gallium garnets." Physical Review 156, no. 2 (1967): 663. https://doi.org/10.1103/PhysRev.156.663 36 53. Danuta Piwowarska, Paweł Gnutek, and Czesław Rudowicz. "Origin of the Ground Kramers Doublets for Co2+ (3d7) Ions with the Effective Spin 3/2 Versus the Fictitious ‘Spin’½." Applied Magnetic Resonance 50, no. 6 (2019): 797-808. https://doi.org/10.1007/s00723- 018-1080-4 54. A. Abragam and B. Bleaney. Electron paramagnetic resonance of transition ions. Clarendon press Oxford, 1970. 55. See Supplemental Material at [URL] for “Spin state crossover in Co3BO5”. 56. G.M. Cai, L. Wang, L.M. Su, H.S. Liu, and Z.P. Jin. "Subsolidus phase relations in CoO– In2O3–B2O3 system and crystal structure of Co3-xInxBO5 solid solution for 0< x 1." Journal of Alloys and Compounds 615 (2014): 809-816. ⩽ 57. R.M. Wood and G.J. Palenik, Bond Valence Sums in Coordination Chemistry. A Simple Method for Calculating the Oxidation State of Cobalt in Complexes Containing Only Co-O Bonds, Inorg. Chem. 1998, 37, 4149-4151. 58. N.V. Kazak, M.S. Platunov, Yu.V. Knyazev, E.M. Moshkina, L.A. Solovyov, S.N. Vereshchagin, Yu.L. Mikhlin, A.A. Veligzhanin, A.L. Trigub, and S.G. Ovchinnikov. "Study of mixed-valence Mn2BO4 using XRD, XPS and XAFS spectroscopies." Physica B: Condensed Matter 560 (2019): 228-235. 59. Yu.S. Orlov, L.A. Solovyov, V.A. Dudnikov, A.S. Fedorov, A.A. Kuzubov, N.V. Kazak, V.N. Voronov et al. "Structural properties and high-temperature spin and electronic transitions in GdCoO3: Experiment and theory." Physical Review B 88, no. 23 (2013): 235105. 60. Tachibana, Makoto, Takahiro Yoshida, Hitoshi Kawaji, Tooru Atake, and Eiji Takayama- Muromachi. "Evolution of electronic states in RCoO3 (R= rare earth): Heat capacity measurements." Physical Review B 77, no. 9 (2008): 094402. 61. K. Knizek, Z. Jirak, J. Hejtmanek, M. Veverka, M. Marysko, G. Maris, T.T.M. Palstra. Structural anomalies associated with the electronic and spin transitions in LnCoO3// European Physical Journal B. – 2005. – V.47. – P. 213 – 220. 62. B. Raveau and Md.M. Seikh, Cobalt Oxides. From Crystal Chemistry to Physics, Wiley- VCH, Weinheim, Germany (2012). 63. N.B. Ivanova, S.G. Ovchinnikov, M.M. Korshunov, and N.V. Kazak. "Specific features of spin, charge, and orbital ordering in cobaltites." Physics-Uspekhi 52, no. 8 (2009): 789. 64. Yu.S. Orlov, V.A. Dudnikov, M.V. Gorev, S.N. Vereshchagin, L.A. Solov’ev, and S.G. Ovchinnikov. "Thermal properties of rare earth cobalt oxides and of La1–xGdxCoO3 solid solutions." JETP letters 103, no. 9 (2016): 607-612. 37 65. Yang, Tao, Ying Wang, Dingfeng Yang, Guobao Li, and Jianhua Lin. "Field-induced spin- flop-like metamagnetism in α-CoB4O7." Solid state sciences 19 (2013): 32-35. 66. S.C. Neumair, J.S. Knyrim, R. Glaum, and H. Huppertz. "High‐Pressure Syntheses, Crystal Structures, and Properties of the Transition Metal Borates β‐MB4O7 (M= Fe, Co)." Zeitschrift für anorganische und allgemeine Chemie 635, no. 12 (2009): 2002-2008. 67. S.C. Neumair, R. Kaindl, and H. Huppertz. "Synthesis and crystal structure of the high- pressure cobalt borate HP-CoB2O4." Zeitschrift für Naturforschung B 65, no. 11 (2010): 1311-1317. 68. J.C. Joubert, T. Shirk, W. B. White, and R. Roy. "Stability, infrared spectrum and magnetic properties of FeBO3." Materials Research Bulletin 3, no. 8 (1968): 671-676. 69. A.D. Balaev, N.B. Ivanova, N.V. Kazak, S.G. Ovchinnikov, V.V. Rudenko, and V.M. Sosnin. "Magnetic anisotropy of the VBO3 and CrBO3 transition-metal borates." Physics of the Solid State 45, no. 2 (2003): 287-291. 70. M. Huber, and H.J. Deiseroth. "Crystal structure of titanium (III) borate, TiBO3." Zeitschrift fur Kristallographie 210, no. 9 (1995): 685-685. 71. V. Ragupathi, M. Safiq, P. Panigrahi, T. Hussain, S. Raman, R. Ahuja, and G. S. Nagarajan. "Enhanced electrochemical performance of LiMnBO3 with conductive glassy phase: a prospective cathode material for lithium-ion battery." Ionics 23, no. 7 (2017): 1645-1653. 72. A. Utzolino, K. Bluhm. "New Insights into the Stabilization of the Hulsite Structure During Crystal Structure Determination of MnII2MnIII(BO3)O2 and MnIISrMnIII(BO3)O2." Zeitschrift für Naturforschung B 51, no. 10 (1996): 1433-1438. 73. R. Wolfe, R.D. Pierce, M. Eibschütz, and J.W. Nielsen. "Magnetization and Mössbauer effect in single crystal Fe3BO6." Solid State Communications 7, no. 13 (1969): 949-952. 74. X. Zeng, Q. Kuang, Q. Fan, Y. Dong, Y. Zhao, S. Chen, and S. Liu. "Synthesis, structure, and electrochemical performance of V3BO6 nanocomposite: A new vanadium borate as high-rate anode for Li-ion batteries." Electrochimica Acta (2020): 135661. 75. J.L.C. Rowsell and L.F. Nazar. "Synthesis, structure, and solid-state electrochemical properties of Cr3BO6: a new chromium (III) borate with the norbergite structure." Journal of Materials Chemistry 11, no. 12 (2001): 3228-3233. 76. N.V. Kazak, N.B. Ivanova, V.V. Rudenko, S.G. Ovchinnikov, A.D. Vasil’ev, and Yu.V. Knyazev. "Conductivity study of Co3O2BO3 and Co3-xFexO2BO3 oxyborates." In Solid State Phenomena, vol. 152, pp. 104-107. Trans Tech Publications Ltd, 2009. 38